A Matching Problem, Partial Order, and an Analysis Applying the Copeland Index

Abstract

Given two sets A and B, often the question arises how far objects a of A and b of B can be combined to a pair (a,b), fulfilling certain requirements. A first example is the marriage problem, another, the successful assignment of scientific projects to the needs of small or medium-sized enterprises. A third example, which motivated this study, arises from the project iBaMs–Barriere-Reduced Machines in Innovative Interaction. This project was aiming at promoting social inclusion for people with intellectual disabilities and their integration into labor markets and everyday activities. Especially, the project iBaMs “examines the preconditions and requirements for the development of control panels for computer-numerical-controlled (CNC) machines” (Wiesner-Steiner et al., Proceedings of the International Conferences Interfaces and Human Computer Interaction 2014, Game and Entertainment Technologies 2014, and Computer Graphics, Visualization, Computer Vision and Image Processing, pp 54–61, 2014). On the one hand, different control panels can be identified and characterized by a set of indicators. On the other hand, classifications of people with intellectual disabilities are available, leading to a profile of skills. The question arises on how optimal control panels based on indicators can be assigned to the profile of skills of employees. This assignment is called a matching between optimal control panels and profiles of skills. A first approach will be discussed on how this matching can be performed. It turns out that the Copeland index (Al-Sharrah J Chem Inf Model 50(5):785–791, 2010; Saari and Merlin, J Econ Theory 8:51–76, 1996) in its simplified form can be applied to answer the question.